arXiv subjects

Ábel Göde

Publications and source records attributed to Ábel Göde.

3 recordsLinked to original sources

arXiv2026

Operators on anti-dual pairs: Means of positive operators

We develop a theory of Kubo-Ando type means for positive operators on anti-dual pairs. This framework extends the classical theory of operator means beyond bounded Hilbert space operators and provides a common setting for several concrete classes of positive objects, including nonnegative sesquilinear forms and states on $C^*$-algebras. We also introduce a Busch-Gudder type strength function for positive operators on anti-dual pairs and investigate its interaction with operator means. Applications are given to Hilbert space operators, nonnegative forms, and representable positive functionals.

math.FA↗

arXiv2024

Operators on anti-dual pairs: Lebesgue decomposition via Arlinskii's iteration

The aim of this paper is to prove a general Lebesgue decomposition theorem for positive operators on so-called anti-dual pairs, following the iterative approach introduced by Arlinskii. This procedure and the resulting theorem encompass several special cases, including positive operators on Hilbert spaces, non-negative forms on vector spaces, and representable functionals over *-algebras.

math.FA↗

arXiv2023

Operators on anti-dual pairs: Supremum and infimum of positive operators

Our purpose in this note is to investigate the order properties of positive operators from a locally convex space into its conjugate dual. We introduce a natural generalization of the Busch-Gudder strength function and we prove Kadison's anti-lattice theorem and Ando's result on the infimum of positive operators in that context.

math.FA↗